4 hours ago = 1,000
2 hours ago = 2,000
Now = 4,000
In 2 hours = 8,000
In 4 hours = 16,000
In 6 hours = 32,000
In 8 hours = 64,000
In 10 hours = 128,000
In 12 hours = 256,000
The answer would be D. 12 hours.
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A polynomial function has exactly four zeros: 4, 2, √2 and -√2. What degree would this polynomial have? Show ALL work.
Answer:
Fourth degree polynomial (aka: quartic)
====================================================
Work Shown:
There isnt much work to show here because we can use the fundamental theorem of algebra. The fundamental theorem of algebra states that the number of roots is directly equal to the degree. So if we have 4 roots, then the degree is 4. This is assuming that there are no complex or imaginary roots.
-------------------
If you want to show more work, then you would effectively expand out the polynomial
(x-m)(x-n)(x-p)(x-q)
where
m = 4, n = 2, p = sqrt(2), q = -sqrt(2)
are the four roots in question
(x-m)(x-n)(x-p)(x-q)
(x-4)(x-2)(x-sqrt(2))(x-(-sqrt(2)))
(x-4)(x-2)(x-sqrt(2))(x+sqrt(2))
(x^2-6x+8)(x^2 - 2)
(x^2-2)(x^2-6x+8)
x^2(x^2-6x+8) - 2(x^2-6x+8)
x^4-6x^3+8x^2 - 2x^2 + 12x - 16
x^4 - 6x^3 + 6x^2 + 12x - 16
We end up with a 4th degree polynomial since the largest exponent is 4.
John and Ling start their new jobs on the same day. John's schedule is 4 workdays followed by 1 day off. Ling's schedule is 7 workdays followed by 2 days off. On how many days during their first year of work (365 days) do John and Ling have the same day off?
Answer:16 days
Step-by-step explanation:
Given
John schedule is 4 Workdays and 5 th day off i.e. John take holiday at the 5 th day
Ling Work for 7 day and then took off on 8 th and 9 th day
i.e. after every 8 th and 9 th day he take off
So to find out common day off we nee take LCM of
i)5 and 8
ii)5 and 9
LCM(5,8)=40 i.e. after every 40 th day they had same day off
and there are 8 such days in 365 days
LCM(5,9)=45 i.e. after every 45 day they had same day off
and there are total of 8 days in 365 days
therefore there are total of 16 days in total out of 365 days
By computing the LCM of their work schedules, John and Ling will have the same day off 8 times during their first year of work.
Explanation:This problem can be approached using the concept of Least Common Multiple (LCM) which is widely used in mathematics to solve similar problems. Here we need to calculate the frequency of John and Ling's common days off.
John's schedule repeats every 5 days (4 workdays followed by 1 day off) and Ling's schedule repeats every 9 days (7 workdays followed by 2 days off). To know how often they both have a day off on the same day, we need to find the LCM of 5 and 9. Interestingly, since 5 and 9 are prime to each other, their LCM will be their product, which is 45. Therefore, John and Ling will have a day off together every 45 days.
To know how many such days will be there in a year, divide 365 by 45 which equals 8.111. Since the number of days cannot be fractional, we take only the whole number part which is 8. So, during the first year of their work (365 days), John and Ling will have the same day off on 8 days.
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A strip mall generates $215,000 in effective rental income and $3,000 in other income. The same mall has $102,000 in operating expenses and $15,000 as reserves. What is the net operating income ofthe strip mall?
A. $113,000
B. $99,000
C. $101,000
D. $116,000
Answer: $116,000
Step-by-step explanation:
The net operating income will be the operation profit after deducting the expenses from the accrued revenue (reserve exclusive)
The revenue generated are $215,000 + $3,000
= $218,000
Expenses incurred;
$102,000
The net operating income = $218,000 - $102,000
= $116,000
Note that reserves is not used in business operation. Therefore it cannot be regarded either as revenue or expenses.
What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the spread of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.
Answer:
No, the student is not right as his statement is against central limit theorem.
Step-by-step explanation:
Central Limit Theorem:
This theorem states that if we take large samples of a population which has a mean and standard deviation then mean samples will have a normal distribution.
So the statement of this theorem negates the statement of the boy who said that the spread of sampling distribution of the sample mean will decrease.You have a triangle that has an altitude 5 inches longer than the base.If the area of your triangle is 63 square inches, what are the dimensions of the base and altitude?
Answer:
Base of triangle is 9 inches and altitude of triangle is 14 inches.
Step-by-step explanation:
Given:
Area of Triangle = 63 sq. in.
Let base of the triangle be 'b'.
Let altitude of triangle be 'a'.
Now according to question;
altitude is 5 inches longer than the base.
hence equation can be framed as;
[tex]a=b+5[/tex]
Now we know that Area of triangle is half times base and altitude.
Hence we get;
[tex]\frac{1}{2} \times b \times a =\textrm{Area of Triangle}[/tex]
Substituting the values we get;
[tex]\frac{1}{2} \times b \times (b+5) =63\\\\b(b+5)=63\times2\\\\b^2+5b=126\\\\b^2+5b-126=0[/tex]
Now finding the roots for given equation we get;
[tex]b^2+14b-9b-126=0\\\\b(b+14)-9(b+14)=0\\\\(b+14)(b-9)=0[/tex]
Hence there are 2 values of b[tex]b-9 = 0\\b=9\\\\b+14=0\\b=-14[/tex]
Since base of triangle cannot be negative hence we can say [tex]b=9\ inches[/tex]
So Base of triangle = 9 inches.
Altitude = 5 + base = 5 + 9 = 14 in.
Hence Base of triangle is 9 inches and altitude of triangle is 14 inches.
Which system of equations can be used to find the roots of the equation 4x5-12x4+6x=5x3-2x?
Answer:
Y=4x^5-12x^4+6x and y=5x^3-2x
Answer:
Y = 4x5 - 12x4 + 6x
Y = 5x3 - 2x
Step-by-step explanation:
A cab in NYC charges you $1.25 a mile and a flat fee of $4 to ride in the cab. A cab in Chicago charges you $0.75 a mile but a flat fee of $6 just to get in the cab. If you paid the same amount of money for a cab ride in each city how many miles would the cab have driven you?
Answer:
After 4 miles driven by cab the amount would be same in both cities.
Step-by-step explanation:
Let the number of miles be 'x'.
Given:
In NYC
Flat fee of cab = $4
Per mile charge = $1.25
Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.
Framing in equation form we get;
Total cab charges in NYC = [tex]4+1.25x[/tex]
In Chicago
Flat fee of cab = $6
Per mile charge = $0.75
Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.
Framing in equation form we get;
Total cab charges in Chicago = [tex]6+0.75x[/tex]
Now we need to find number of miles driven so that the amount could same in both cities.
Total cab charges in NYC = Total cab charges in Chicago
[tex]4+1.25x=6+0.75x[/tex]
Combining like terms we get;
[tex]1.25x-0.75x=6-4\\\\0.5x=2[/tex]
using Division Property we will divide both side by 0.5 we get;
[tex]\frac{0.5x}{0.5} =\frac{2}{0.5} \\\\x=4[/tex]
Hence After 4 miles driven by cab the amount would be same in both cities.
The lowest monthly commission that a salesman earned was only 1/5 more than 1/4 as high as the highest commision he earned. The highest and lowest comissions when added together equal $819. What was the lowest comission?
Answer: the lowest commission is $163.96
Step-by-step explanation:
Let x represent the lowest monthly commission that a salesman earned.
Let y represent the highest monthly commission that a salesman earned.
The lowest monthly commission that a salesman earned was only 1/5 more than 1/4 as high as the highest commission he earned. This means that
x = y/4 + 1/5 - - - - - - - - 1
The highest and lowest commissions when added together equal $819. This means that
x + y = 819
x = 819 - y - - - - - - -2
Substituting equation 2 into 1, it becomes
819 - y = y/4 + 1/5
Multiplying through by 20, it becomes
16380 - 20y = 5y + 4
25y = 16380 - 4 = 16376
y = 16376/25 = 655.04
x = 819 - 655.04 = 163.96
Delete the ribbon is 3/4 meter Sunday needs pieces measuring 1/3 meter for in our project what is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon
Answer:the greatest number of pieces that can be cut is 2
Step-by-step explanation:
The total length of ribbon available is 3/4 meter. Sunday needs pieces measuring 1/3 meter for their project. This means that each length needed would be exactly 1/3 meter.
The number of pieces measuring 1/3 meter that can be cut from the ribbon would be
(3/4)/(1/3) = 3/4×3/1 = 9/4 = 2.25
Since the length needed is exactly 1/3 meter, the greatest number of pieces that can be cut will be 2
When the denominator of \dfrac{2}{\sqrt{3}} 3 2 start fraction, 2, divided by, square root of, 3, end square root, end fraction is rationalized, it becomes \dfrac{2k}{3} 3 2k start fraction, 2, k, divided by, 3, end fraction. Find kkk
Answer:
Step-by-step explanation:
k = 6
To find the value of k, rationalize the denominator of 2/√3, and compare it with 2k/3 to find k = √3.
To rationalize the denominator of the fraction 2/√3, we need to make the denominator a rational number. We can do this by multiplying both the numerator and the denominator by √3.
Multiply the numerator and the denominator by √3:[tex]\frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3} = \frac{2\sqrt3}{3}[/tex]So, after rationalizing, the fraction becomes 2√3/3. According to the problem statement, this is equivalent to 2k/3.
Therefore, we can equate 2k to 2√3:
2k = 2√3
k = √3
So, the value of k is √3.
The complete question is
When the denominator of 2/√3 is rationalized ,it becomes 2k/3. Find k
George and Samantha both applied for a personal loan at Westside Bank. George has a credit score of 650. Samantha has a credit score of 520. The bank approved George’s loan application at 5.6% interest. Samantha was approved for the same loan amount, but, because of her lower credit rating, the interest charged on Samantha’s loan is 3 percentage points higher than the interest rate on George’s loan. What interest rate does Samantha pay to the bank?
A. 8.6%
B. 5.9%
C. 3.0%
D. 2.6%
Option A
Interest rate paid by Samantha to bank is 8.6 %
Solution:
Given that George has a credit score of 650
Samantha has a credit score of 520
The bank approved George’s loan application at 5.6% interest
To find: Interest rate paid by samantha to the bank
From given information in question,
Interest charged on Samantha’s loan is 3 percentage points higher than the interest rate on George’s loan
Thus we get,
Interest charged on Samantha’s loan = 3 percentage points higher than the interest rate on George’s loan
Interest charged on Samantha’s loan = 3 % higher than the interest rate on George’s loan
Interest charged on Samantha’s loan = 3 % + interest rate on George’s loan
Thus substituting the given George’s loan application at 5.6% interest,
Interest charged on Samantha’s loan = 3 % + 5.6 % = 8.6 %
Thus interest rate paid by samantha to bank is 8.6 %
Final answer:
Option A: 8.6%
Samantha will pay an interest rate of 8.6% on her loan from Westside Bank, which is 3 percentage points higher than George's rate of 5.6% due to her lower credit score.
Explanation:
The question involves calculating the interest rate Samantha will pay to the bank for a personal loan.
Given that George has a credit score of 650 and was approved for a loan at 5.6% interest, and Samantha has a lower credit score of 520, her interest rate will be 3 percentage points higher than George's.
To find Samantha's interest rate, we simply add 3 percentage points to George's rate of 5.6%.
Samantha's interest rate = George's interest rate + 3%
Samantha's interest rate = 5.6% + 3%
Samantha's interest rate = 8.6%
Area addition and subtraction
Answer:
3.8 [tex]in^{2}[/tex]
Step-by-step explanation:
We are given a square of size 6x6 in. So, area of this square is equal to 6 x 6 = 36 [tex]in^{2}[/tex]. Now, the shaded region is [tex]\frac{1}{2}[/tex] x (Area of square - area of semicircles)
The diameter of both semicircles = side of the square = 6in
So, radius (r) = [tex]\frac{1}{2}[/tex] x diameter = [tex]\frac{1}{2}[/tex] x 6 = 3in
And hence, area of semicircle is = [tex]\frac{1}{2}[/tex] x π[tex]r^{2}[/tex]
= [tex]\frac{1}{2}[/tex] x π[tex]3^{2}[/tex]
Since, there are two semicircles we multiply above by 2, so area of both semicircles = 2 x [tex]\frac{1}{2}[/tex] π[tex]3^{2}[/tex] = 9π
Area of shaded region = [tex]\frac{1}{2}[/tex] (36 - 9π) = 3.8628 = 3.8 [tex]in^{2}[/tex] to the nearest tenth.
Find the product of (x-7)^2 and explain how it demonstrates the closure property of multiplication
A. X^2-14x+49; is a polynomial
B. X^2-14x+49; may or may not be a polynomial
C. X^2-49; is a polynomial
D. X^2-49; may or may not be a polynomial
A. x²-14x+49; is a polynomial
Step-by-step explanation:
(x-7)² can be written as (x-7)(x-7)
Expanding the expression
x(x-7)-7(x-7)
x²-7x-7x+49
x²-14x+49 ⇒⇒A quadratic function, which is a polynomial of degree 2
This function demonstrates the closer property of multiplication in that the change in order of multiplication does not change the product. This is called commutative property.
(x-7)(x-7)
-7(x-7)+x(x-7)
-7x+49+x²-7x
x²-14x+49
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Answer:
A is correct
Step-by-step explanation:
I took the test and got it right
Mr Thomson wants to protect his garage by installing a flood barrier.He connects two barriers side by side.Each barrier is 9 feet long by 2 feet high.What is the combined area of the barriers?
Answer:
36 square feet
Step-by-step explanation:
The area of one barrier is the product of the given dimensions:
(9 ft)(2 ft) = 18 ft²
Two such barriers will have twice the area: 36 ft².
The combined area of the two barriers is calculated by multiplying the length by the height for each barrier to get an area for each one, and then those two areas are added together. Each barrier has an area of 18 square feet, so the total combined area is 36 square feet.
Explanation:The question is asking for the combined area of two barriers, each being 9 feet long and 2 feet high. In order to find this, we must multiply the length by the height for each barrier, and then add these two areas together. The calculation would look like this:
Area of each barrier = Length x Height = 9 ft x 2 ft = 18 square feet
Now, since there are two barriers:
Combined Area = 2 x Area of each barrier = 2 x 18 square feet = 36 square feet
Therefore, the combined area of the two barriers is 36 square feet.
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The whitish distance across the scale model of the planet Venus is 15 cm. The actual widest distance across Venus is approximately 12,000 km. What is the scale of the Model of Venus
Answer:
1 cm : 800 km or 1/80,000,000
Step-by-step explanation:
A model or map scale is often expressed as ...
(1 unit of A on the model) : (N units of B in the real world)
We're given the relative measurements as ...
15 cm : 12,000 km
Dividing by 15 gives the unit ratio as above:
1 cm : 800 km
__
A scale can also be expressed as a unitless fraction. To find that, we need to convert the units of both parts of this ratio to the same unit.
0.01 m : 800,000 m
Multiplying by 100, we get ...
1 m : 80,000,000 m
Since the units are the same, they aren't needed, and we can write the scale factor as ...
1 : 80,000,000 or 1/80,000,000
Attachment below
algebra helppppp
Answer: second option.
Step-by-step explanation:
In order to solve this exercise, it is necessary to remember the following properties of logarithms:
[tex]1)\ ln(p)^m=m*ln(p)\\\\2)\ ln(e)=1[/tex]
In this case you have the following inequality:
[tex]e^x>14[/tex]
So you need to solve for the variable "x".
The steps to do it are below:
1. You need to apply [tex]ln[/tex] to both sides of the inequality:
[tex]ln(e)^x>ln(14)[/tex]
2. Now you must apply the properties shown before:
[tex](x)ln(e)>ln(14)\\\\(x)(1)>2.63906\\\\x>2.63906[/tex]
3. Then, rounding to the nearest ten-thousandth, you get:
[tex]x>2.6391[/tex]
There are blue,yellow and green cubes in a bag. There are 3 times as many blue cubes as yellow and five times as many green cubes as blue cubes.What is the probability that a yellow cube is taken out of a bag.
Answer: 5/7
Step-by-step explanation:please see attachment for explanation.
Some friends are making cookies for a bake sale. In all they need 6 cups of flour however they only have a 1/4 measuring cup. How many time will they need to fill the measuring cup
Answer:
24 times
Step-by-step explanation:
Given:
Number of cups required = 6 cups
Measuring cup capacity = [tex]\frac{1}{4}=0.25[/tex] of a cup.
Now, each time the measuring cup fills 0.25 of a cup.
So, we use unitary method to find the number of times the measuring cup has to be used to get a total of 6 cups.
∵ 0.25 cups = 1 time the measuring cup being used.
∴ 1 cup = [tex]\frac{1}{0.25}=4[/tex] times the measuring cup being used.
So, 6 cups = [tex]4\times 6=24[/tex] times the measuring cup being used.
Hence, the number of times the measuring cup has to be used to get 6 cups of flour is 24 times.
John is 4 years older than Becky, and John’s and Becky’s combined ages is 58. How old are Becky and John?A. Becky is 26; John is 32 B. Becky is 26; John is 30 C. Becky is 27; John is 31 D. Becky is 25; John is 29
Answer:
Answer C: Becky is 27; John is 31
Step-by-step explanation:
1. John is 4 years older than Becky--27(Becky's age)+ 4=31(John's age)
2. Sum of their ages is 58--27(Becky's age)+31(John's age)=58
So, the correct answer is Answer C.
Answer:
C. Becky is 27; John is 31
City Cab charges a flat fee of $3 plus 0.50 per mile. Henry paid $10.50 for a cab ride across town. The equation 3 + 0.50m = 10.50 represents Henry's cab ride, where m is number of miles traveled. How many miles did Henry travel?
Answer:the number of miles that Henry traveled is 15
Step-by-step explanation:
Let m represent the number of miles travelled.
City Cab charges a flat fee of $3 plus 0.50 per mile. This means that the total amount that city Cab charges for m miles would be
3 + 0.5m
Henry paid $10.50 for a cab ride across town.
The equation representing Henry's cab ride would be
3 + 0.50m = 10.50
Subtracting 3 from both sides of the equation, it becomes
3 - 3 + 0.50m = 10.50 - 3
0.5m = 7.5
m = 7.5/0.5 = 15 miles
PLEASE ANSWER! Given the functions f(x) = x2 + 6x - 1, g(x) = -x2 + 2, and h(x) = 2x2 - 4x + 3, rank them from least to greatest based on their axis of symmetry.
a. f(x), g(x), h(x)
b. h(x), g(x), f(x)
c. g(x), h(x), f(x)
d. h(x), f(x), g(x)
Answer:
he rank from least to great based on their axis of symmetry:
0, 1, -3 ⇒ g(x), h(x), f(x)
So, option C is correct.
Step-by-step explanation:
A quadratic equation is given by:
[tex]ax^2+bx+c =0[/tex]
Here, a, b and c are termed as coefficients and x being the variable.
Axis of symmetry can be obtained using the formula
[tex]x = \frac{-b}{2a}[/tex]
Identification of a, b and c in f(x), g(x) and h(x) can be obtained as follows:
[tex]f(x) = x^2 + 6x - 1[/tex]
⇒ a = 1, b = 6 and c = -1
[tex]g(x) = -x^2 + 2[/tex]
⇒ a = -1, b = 0 and c = 2
[tex]h(x) = 2^2 - 4x + 3[/tex]
⇒ a = 2, b = -4 and c = 3
So, axis of symmetry in [tex]f(x) = x^2 + 6x - 1[/tex] will be:
[tex]x = \frac{-b}{2a}[/tex]
x = -6/2(1) = -3
and axis of symmetry in [tex]g(x) = -x^2 + 2[/tex] will be:
[tex]x = \frac{-b}{2a}[/tex]
x = -(0)/2(-1) = 0
and axis of symmetry in [tex]h(x) = 2^2 - 4x + 3[/tex] will be:
[tex]x = \frac{-b}{2a}[/tex]
x = -(-4)/2(2) = 1
So, the rank from least to great based on their axis of symmetry:
0, 1, -3 ⇒ g(x), h(x), f(x)
So, option C is correct.
Keywords: axis of symmetry, functions
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The coordinates of the endpoints of line AB are graphed in the standard (x, y) coordinate plane at (10, 14) and (4, -2). What is the y-coordinate of the midpoint of line AB?
y coordinate of midpoint of line AB is 6
Solution:
Given that endpoints of line AB is (10, 14) and (4, -2)
To find: y-coordinate of the midpoint of line AB
The midpoint of line AB is given as:
For a containing [tex]A(x_1, y_1)[/tex] and [tex]B(x_2, y_2)[/tex] the midpoint is given as:
[tex]M(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this question,
[tex]\left(x_{1}, y_{1}\right)=(10,14) \text { and }\left(x_{2}, y_{2}\right)=(4,-2)[/tex]
So midpoint is:
[tex]\begin{aligned}&M(x, y)=\left(\frac{10+4}{2}, \frac{14-2}{2}\right)\\\\&M(x, y)=\left(\frac{14}{2}, \frac{12}{2}\right)\\\\&M(x, y)=(7,6)\end{aligned}[/tex]
Therefore y coordinate of midpoint of line AB is 6
Evaluate 2(4 – 1)^2
plz hurry i’ll give best if right
To evaluate the expression 2(4 - 1)^2, multiply 2 by the square of the result of subtracting 1 from 4, resulting in 18.
Explanation:To evaluate the expression 2(4 - 1)^2, we need to follow the order of operations, also known as PEMDAS. First, we evaluate the expression within the parentheses: 4 - 1 = 3. This gives us 2(3)^2. Next, we calculate the exponential expression: 3^2 = 9. Finally, we multiply 2 by 9, which gives us the final result of 18.
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Raquel measured milk with a 1/2-cup measuring cup. She filled the cup 5 times and poured each 1/2-cup of milk in a bowl. How much milk did Raquel pour into the bowl?
Answer:
2 1/2 cups
Step-by-step explanation:
5 × (1/2 cup) = 5/2 cup = 2 1/2 cup
__
Or, you can add them up. You know from your study of fractions that two half-cups make 1 cup.
(1/2 cup) + (1/2 cup) + (1/2 cup) + (1/2 cup) + (1/2 cup)
= ((1/2 cup) +(1/2 cup)) +((1/2 cup) +(1/2 cup)) +(1/2 cup)
= (1 cup) + (1 cup) + (1/2 cup)
= (2 cup) + (1/2 cup)
= 2 1/2 cup
A construction worker needs to put in a rectangular window in the side of a building. He knows from measuring that the top and bottom of the window has a width of 5ft and the sides have a length of 12ft. He also measured a diagonal of 13 ft. What is the length of the other diagonal?
Answer:
13
Step-by-step explanation:
The diagonals of a rectangle are congruent.
In a particular game of chance, a wheel consists of 42 slots numbered 00, 0, 1, 2,...,40. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Determine the sample space for one spin of this game.
Answer:
The sample space for one spin of this game is: S = {00, 0, 1, 2, 3,…, 40}
Step-by-step explanation:
Consider the provided information.
In probability theory, the set of all possible outcomes or outcomes of that experiment is the sample space of an experiment or random trial. Using set notation, a sample space is usually denoted and the possible ordered outcomes are identified as elements in the set.
Here the possible number of elements in the set are 00, 0, 1, 2,...,40
The sample space is anything the ball can land on.
Thus, the sample space for one spin of this game is: S = {00, 0, 1, 2, 3,…, 40}
Pls help me thank you !!
I think 68 or56
It can't be 34 that would be less, 146 would be over quarter
Good evening ,
Answer:
measure arc AB = 68°
Step-by-step explanation:
measure arc AB = 2×(m∠AXB) = 2×(34) = 68°.
:)
What is an equation of the parabola with vertex at the origin and focus (-5,0)?
The equation of parabola is expressed as: y² = -20x
What is the equation of the parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.
The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
Given, vertex = (0, 0)
Focus = (-5, 0)
We have to find the equation of the parabola.
The equation is of the form y = -ax²
Directrix x = 5.
As every point on parabola is equidistant from focus and directrix, the equation will be
y² + (x + 5)² = (x - 5)²
y² + x² + 10x + 25 = x² - 10x + 25
y² = - 10x - 10x
y² = -20x
Therefore, the equation of parabola is y² = -20x
At the city museumy child admission is and admission is $9.30. On Monday four times as many adult tickets as child tickets were sold for a total of sales of $1548.00 . How many child tickets were sold that day.
Answer:
The number of child tickets sold was 36
Step-by-step explanation:
The complete question is
At the city museum, child admission is $5.80 and adult admission is $9.30. On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1548.00. How many child tickets were sold that day?
Let
x ----> the number of child tickets sold
y ----> the number of adult tickets sold
we know that
[tex]5.80x+9.30y=1,548.00[/tex] ---> equation A
[tex]y=4x[/tex] ----> equation B
Solve by substitution
Substitute equation B in equation A
[tex]5.80x+9.30(4x)=1,548.00[/tex]
solve for x
[tex]5.80x+37.2x=1,548.00[/tex]
[tex]43x=1,548.00[/tex]
[tex]x=36[/tex]
therefore
The number of child tickets sold was 36
Need help with two questions I am not good with this
Answer:
Part 12) [tex]Center\ (2,-3),r=2\ units, (x-2)^2+(y+3)^2=4[/tex]
Part 13) [tex]m\angle ABC=47^o[/tex]
Step-by-step explanation:
Part 12) we know that
The equation of a circle in center-radius form is equal to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where
(h,k) is the center of the circle
r is the radius of the circle
In this problem
Looking at the graph
The center is the [tex]point\ (2,-3)[/tex]
The radius is [tex]r=2\ units[/tex]
substitute in the expression above
[tex](x-2)^2+(y+3)^2=2^2[/tex]
[tex](x-2)^2+(y+3)^2=4[/tex]
Part 13) we know that
The measure of the external angle is the semi-difference of the arcs it covers.
so
[tex]m\angle ABC=\frac{1}{2}[arc\ DE-arc\ AC][/tex]
we have
[tex]arc\ DE=142^o[/tex]
[tex]arc\ AC=48^o[/tex]
[tex]m\angle ABC=\frac{1}{2}[142^o-48^o][/tex]
[tex]m\angle ABC=47^o[/tex]